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Model Paper 8 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 81 Mark
MCQ
If 3 sin x + 4 cos x = 5, then 4 sin x - 3 cos x =
  • A
    1
  • B
    5
  • C
    3
  • D
    $0$
✓

Answer

(d) 0
Explanation: 3 sinx + 4 cosx = 5
$\frac{3}{5} \sin x+\frac{4}{5} \cos x=1$
Let $\cos \alpha=\frac{3}{5}$ and $\sin \alpha=\frac{4}{5}$
$\therefore \cos \alpha \sin x+\sin \alpha \cos x=1$
$\begin{array}{l}\Rightarrow \sin (\alpha+x)=\sin \frac{\pi}{2} \\ \Rightarrow \alpha+x=\pi \\
\Rightarrow x=\frac{\pi}{2}-\alpha \ldots . \text { (i) }\end{array}$
We have to find the value of 4 sin x - 3 cos x
$4 \sin \left(\frac{\pi}{2}-\alpha\right)-3 \cos \left(\frac{\pi}{2}-\alpha\right) \ldots$. From eq. (i)
$\begin{array}{l}=4 \cos \alpha-3 \sin \alpha \\ =4 \times \frac{3}{5}-3 \times \frac{4}{5}\left(\because \cos \alpha=\frac{3}{5} \text { and } \sin \alpha=\frac{4}{5}\right) \\ 0\end{array}$

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